I.  Abstract

This part of the OGC Simple Features (SF) Standard describes an encoding of Simple Features (per Part 1) in a Well-Known Text (WKT) Representation. Each Geometry Type has a Well-known Text Representation that can be used both to construct new instances of the type and to convert existing instances to textual form for alphanumeric display.

III.  Preface

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. The Open Geospatial Consortium shall not be held responsible for identifying any or all such patent rights.

Recipients of this document are requested to submit, with their comments, notification of any relevant patent claims or other intellectual property rights of which they may be aware that might be infringed by any implementation of the standard set forth in this document, and to provide supporting documentation.

1.  Scope

The Well-Known Text Representation for Geometry (WKTGeometry) provides provides a portable representation of a geometric object that can be used both to construct new instances of the type and to convert existing instances to textual form for alphanumeric display.

2.  Conformance

*NOTE TO EDITORS* Conformance for Parts 1-3 was defined in the original Simple Features Access Part 1 document as follows.

“In order to conform to this standard, an implementation shall satisfy the requirements of one or more test suites specified in the other parts of ISO 19125.”

Meaning that the SQL Part (or legacy CORBA and others) had Abstract Test Suites. We must consider whether to genericize those Test Suites to something for these parts.

*END NOTE*

3.  Normative references

The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.

ISO/IEC: ISO/IEC 13249-3:2016, Information technology — Database languages — SQL multimedia and application packages — Part 3: Spatial. International Organization for Standardization, International Electrotechnical Commission, Geneva (2016). https://www.iso.org/standard/60343.html.

ISO: ISO 19107:2019, Geographic information — Spatial schema. International Organization for Standardization, Geneva (2019). https://www.iso.org/standard/66175.html.

ISO: ISO 19111:2019, Geographic information — Referencing by coordinates. International Organization for Standardization, Geneva (2019). https://www.iso.org/standard/74039.html.

ISO: ISO 19133:2005, Geographic information — Location-based services — Tracking and navigation. International Organization for Standardization, Geneva (2005). https://www.iso.org/standard/32551.html.

OGC Simple Features — Part 1: Architecture

4.  Terms and definitions

This document uses the terms defined in OGC Policy Directive 49, which is based on the ISO/IEC Directives, Part 2, Rules for the structure and drafting of International Standards. In particular, the word “shall” (not “must”) is the verb form used to indicate a requirement to be strictly followed to conform to this document and OGC documents do not use the equivalent phrases in the ISO/IEC Directives, Part 2.

This document also uses terms defined in the OGC Standard for Modular specifications (OGC 08-131r3), also known as the ‘ModSpec’. The definitions of terms such as standard, specification, requirement, and conformance test are provided in the ModSpec.

For the purposes of this document, the following additional terms and definitions apply.

This document uses the terms defined in Sub-clause 5.3 of OGC 06-121r9, which is based on the ISO/IEC Directives, Part 2, Rules for the structure and drafting of International Standards. In particular, the word “shall” (not “must”) is the verb form used to indicate a requirement to be strictly followed to conform to this standard.

For the purposes of this document, the following additional terms and definitions apply.

set that represents the limit of an entity

[SOURCE: ISO 19107:2019]

Clause 4.15 that contains all direct positions whose distance from a specified geometric object is less than or equal to a given distance

[SOURCE: ISO 19107:2019]

union of the interior and boundary of a topological or geometric object

[SOURCE: ISO 19107:2019]

one of a sequence of n-numbers designating the position of a Clause 4.19 in n-dimensional space

[SOURCE: ]

number of measurements or axes needed to describe a position in a Clause 4.7

[SOURCE: ISO 19107:2019]

Clause 4.7 that is related to the real world by a datum

set of mathematical rules for specifying how coordinates are to be assigned to each Clause 4.19

[SOURCE: ISO 19111:2019]

topological 1-dimensional Clause 4.16, representing the continuous image of a line

The term “1-dimensional” refers to the topological dimension of the primitive. In this case, it means that each point not on the boundary is an element in a topological open set within the curve which is isomorphic to an open interval (0, 1). For this standard, the coordinate dimension can be 2 (for x and y), 3 (with z or m added), or 4 (with both z and m added). The ordinates x, y and z are spatial, and the ordinate m is a measure.

[SOURCE: ISO 19107:2019]

position described by a single set of coordinate within a Clause 4.6

[SOURCE: ISO 19107:2019]

last Clause 4.19 of a Clause 4.8

[SOURCE: ISO 19107:2019]

difference between the universe and the Clause 4.3

[SOURCE: ISO 19107:2019]

abstraction of real world phenomena

characteristic of a Clause 4.12

set of disjoint geometric primitives where the Clause 4.1 of each geometric primitive can be represented as the union of other geometric primitives of smaller dimension within the same set

Geometric complexes are often referred to as clean geometry or implicit topology, meaning that the various topological inconsistencies have usually been removed to obtain the “completeness” of the boundary representation.

[SOURCE: ISO 19107:2019]

spatial object representing a geometric set

Regardless of the representation, the feature is usually assumed to be topologically closed, in that points on the boundary of the feature are assumed to belong to the feature, even though those points may not explicitly be represented in the geometric object. When representing a topological entity, geometric objects are assumed to not contain their boundaries.

[SOURCE: ISO 19107:2019]

Clause 4.15 representing a single, connected, homogeneous element of space

[SOURCE: ISO 19107:2019]

set of all direct positions that are on a Clause 4.15 but which are not on its Clause 4.1

[SOURCE: ISO 19107:2019]

also linear positioning system

positioning system that measures distance from a reference point along a route (feature)

[SOURCE: ISO 19133:2005]

topological 0-dimensional Clause 4.16 representing a position

[SOURCE: ISO 19107:2019]

Clause 4.12 with all geometric attributes described piecewise by straight line or planar interpolation between sets of points

For curves, each part (called a “segment” in ISO 19107) has two control points $P_0$ (the “start point”) and $P_1$ (the “end point”). Any other $P$ on the segment can be described using a real number parameter $t$ between 0.0 and 1.0 in the “vector” equation: $P=t{P}_0+(1-t)P_1$.\

For surfaces, each part (called a “patch” in ISO 19107) can be viewed as a polygon which can be broken into triangles each with three control points $P_0$, $P_1$ and $P_2$. Any other $P$ in the triangle can be described using 3 non-negative real numbers whose sum is 1.0 (called “barycentric coordinates”) $a,b,c\in D$; $a,b,c>0$; $a+b+c=1.0$ in the vector equation: $P=a{P}_0+b{P}_1+c{P}_2$.

[[start=point]] === start point

first Clause 4.19 of a Clause 4.8

[SOURCE: ISO 19107:2019]

topological 2-dimensional Clause 4.16 (4.15), locally representing a continuous image of a region of a plane

[SOURCE: ISO 19107:2019]

6.  Conventions

7.  Well-known Text Representation for Geometry

8.  Media Types for any data encoding(s)

A section describing the MIME-types to be used is mandatory for any standard involving data encodings. If no suitable MIME type exists in http://www.iana.org/assignments/media-types/index.html then this section may be used to define a new MIME type for registration with IANA.